Reionisation history. Top: ratio of the mass- and volume-averaged neutral hydrogen fraction. Bottom: volume averaged neutral hydrogen fraction as a function of redshift. In each panel, we show results for the Salpeter IMF (dash-dotted red line) and the evolving IMF (solid dark blue line) models. Grey points indicate observational constraints from: GRB optical afterglow spectrum analyses (light pentagons; Totani et al. 2006, 2014), quasar sightlines (faint squares; Fan et al. 2006) (medium bright circles; Bosman et al. 2022), Lyman-α LFs (dark upward triangles; Konno et al. 2018; Kashikawa et al. 2011; Ouchi et al. 2010; Ota et al. 2010; Malhotra & Rhoads 2004), Lyman-α emitter clustering (dark downwards triangles; Ouchi et al. 2010), the Lyman-α emitting galaxy fraction (dark leftwards triangles; Pentericci et al. 2011; Schenker et al. 2012; Ono et al. 2012; Treu et al. 2012; Caruana et al. 2012, 2014; Pentericci et al. 2014), Lyman-α equivalent widths (dark rightwards triangles; Mason et al. 2018, 2019; Bolan et al. 2022), dark pixels (light squares; McGreer et al. 2015), and damping wings (light diamonds; Davies et al. 2018; Greig et al. 2019).